Goldberg's algorithm
Scaling: iteratively refine by factor 2. Uses BFS-like structure within each phase. Best strongly-polynomial SSSP with negatives.
Advertisement
BMSSP breakthrough (2022)
Bernstein-Nanongkai-Saranurak: Õ(mn^(8/9) log W). First to break Ω(mn) barrier for real-weight negative SSSP.
Advertisement
Practical winners
SPFA (queue-based Bellman-Ford) is fastest in practice for typical inputs. Occasionally beat by highly-optimized Bellman-Ford with heuristics.
No negative cycles assumption
Many advanced algorithms require this. Otherwise no shortest path exists.